Problem: Simplify the following expression: $y = \dfrac{n^2 - 10n + 9}{n - 9} $
Solution: First factor the polynomial in the numerator. $ n^2 - 10n + 9 = (n - 9)(n - 1) $ So we can rewrite the expression as: $y = \dfrac{(n - 9)(n - 1)}{n - 9} $ We can divide the numerator and denominator by $(n - 9)$ on condition that $n \neq 9$ Therefore $y = n - 1; n \neq 9$